Question

The degree of dissociation is 0.4 at 400K and 1 atm for the gaseous reaction $PC{l}_5\left(g\right)\to {PCl}_3\left(g\right)+{Cl}_2\left(g\right)$. Assume ideal behaviour of all the gases, calculate the density (in gm/litre) of mixture at 400K and 0.1 atm $[Atomicwt.ofCl=35.5;UseR=0.08atm-litre/K-mole]$.

• A. 5 g/litre
• B. 4.58 g/litre
• C. 3 g/litre
• D. 8 g/litre

Answer 1

The correct option is B 4.58 g/litre

$PC{l}_5\rightleftharpoons PC{l}_3+C{l}_2$

Initial moles $1$ $0$ $0$

Moles at eqm $1-0.4$ $0.4$ $0.4$

$\therefore$ Total moles at equilibrium= $1-0.4+0.4+0.4=1.4$

$\frac{\text{Normal molecular weight of}PC{l}_5}{\text{Experimental molecular weight of}PC{l}_5}=1+\alpha =1.4$

$\Rightarrow \frac{208.5}{\text{Experimental molecular weight of}PCl-5}=1.4$

$\Rightarrow \text{Experimental molecular weight of}PC{l}_5=\frac{208.5}{1.4}$

Again, $PV=\frac{W}{M}RT$

$\Rightarrow d=\frac{W}{V}=\frac{PM}{RT}=\frac{1\times 208.5}{1.4\times 0.08\times 400}=4.58g/L$